Target Time Mode

Version: v1.6.0-target-time-mode
Release Date: February 2, 2026

Overview

Target Time Mode is an inverse planning feature that allows athletes to plan their race by specifying a desired finish time instead of a base pace. The system calculates the required pacing strategy to achieve the target time while respecting physiological constraints and terrain characteristics.

Key Concept: Forward vs. Inverse Modeling

Forward Model (Traditional): Ability → Pace → Finish Time
- "I can run 6:00/km on flat terrain, what will my finish time be?"
Inverse Model (Target Time Mode): Ability + Target Time → Required Pace Strategy
- "I want to finish in 20 hours, what pacing strategy do I need?"

How It Works

1. Natural Pacing Calculation

The system first calculates natural pacing - what the athlete would naturally do "on autopilot" based on their abilities:

Natural Pacing = f(base_pace, climbing_ability, fitness_level, skill_level, terrain, fatigue)

This represents the predicted finish time if the athlete runs at their natural capability without any specific time goal.

2. Effort Allocation

The system then performs constrained optimization to distribute the time difference (ΔT) across segments:

ΔT = T_natural - T_target

ΔT > 0: Need to go faster than natural pace (requires PUSH effort)
ΔT < 0: Need to go slower than natural pace (requires PROTECT/conservation)
ΔT ≈ 0: Target matches natural ability (STEADY effort)

3. Cost-Weighted Allocation

The optimizer distributes ΔT intelligently based on:

Segment Capacity: How much adjustment is physiologically possible
Effort Cost: How "expensive" each segment is in terms of required effort
Fatigue Multiplier: Early segments are cheaper than late segments
Global Effort Budget: Total deviation is capped by fitness level

Effort Levels

PUSH (Going Faster)

Triggered when: Segment requires ≥10% faster pace than natural

Meaning: This segment requires above-threshold effort to make up time. The athlete must consciously push harder than their natural pace suggests.

Characteristics: - Occurs when target time is aggressive relative to natural ability - Higher metabolic cost and fatigue accumulation - Requires mental focus and effort discipline - Most commonly applied to low-cost segments (flats, easy terrain)

Example: Natural pace is 7:00/km, required pace is 6:20/km or faster (>10% faster)

STEADY (Natural Pace)

Triggered when: Segment adjustment is <10% in either direction

Meaning: Athlete can run at or very close to their natural pace. This is the "cruise control" effort level.

Characteristics: - Sustainable, comfortable effort - Matches athlete's natural ability for the terrain - Minimal mental energy required - Most efficient metabolic profile

Example: Natural pace is 7:00/km, required pace is 6:30-7:30/km (<10% adjustment)

PROTECT (Going Slower)

Triggered when: Segment requires ≥10% slower pace than natural

Meaning: Athlete must actively hold back and conserve energy. This is deliberate pacing restraint.

Characteristics: - Occurs when target time is conservative relative to natural ability - Useful for ultra-distance energy management - Requires discipline to not go too fast - Builds energy reserves for later segments

Example: Natural pace is 7:00/km, required pace is 7:45/km or slower (>10% slower)

How Athlete Abilities Affect Effort

Climbing Ability

Affects: Cost of buying/saving time on climbs

Elite climbers: Climbs are cheap (0.75× cost multiplier)
- Can more easily push harder or ease back on ascents
- Optimizer will preferentially adjust climbing segments
Conservative climbers: Climbs are expensive (1.2× cost multiplier)
- Harder to adjust pace on climbs
- Optimizer will avoid aggressive climb adjustments

Technical Skill

Affects: Cost and capacity on descents

Expert (0.8-1.0): Lower descent cost, wider adjustment range
- Can safely adjust descent pace more aggressively
- Optimizer has more flexibility on downhills
Novice (0.0-0.4): Higher descent cost, narrow adjustment range
- Safety constraints limit descent adjustment
- Even experts face hard caps on descents (risk pricing)

Fitness Level

Affects: Global effort budget (total allowable deviation)

Elite: 50% total deviation budget
- Can sustain larger deviations from natural pace
- More flexibility to hit aggressive targets
Untrained: 15% total deviation budget
- Limited capacity for pace adjustment
- Aggressive targets may be unachievable

Example: For a 20-hour natural finish: - Elite: Can deviate up to 10 hours total across all segments - Untrained: Can deviate up to 3 hours total across all segments

Fatigue (if enabled)

Affects: Cost multiplier increases with cumulative effort

Early segments are cheaper to adjust than late segments:

cost_late = cost_base × fatigue_multiplier

Where fatigue_multiplier grows from 1.0 (start) to 1.05-1.5 (finish) based on fitness level.

Threshold Calculations

Purpose

Thresholds help athletes understand their pacing options: - Upper threshold (PUSH): "If I target this time or faster, I'll need to push" - Lower threshold (PROTECT): "If I target this time or slower, I'll need to hold back" - Between thresholds: Natural pacing zone (STEADY)

Calculation Method

Thresholds are calculated using binary search simulation to find target times where effort transitions occur.

PUSH Threshold

Find the target time where >50% of segments require ≥10% faster adjustment.

Algorithm: 1. Search range: 50% to 100% of natural time 2. For each candidate target time: - Simulate full effort allocation - Count segments with ≥10% faster adjustment 3. Binary search converges when ~50% of segments hit threshold

Interpretation: "Target this time or faster → most segments require PUSH effort"

PROTECT Threshold

Find the target time where >50% of segments require ≥10% slower adjustment.

Algorithm: 1. Search range: 100% to 150% of natural time 2. For each candidate target time: - Simulate full effort allocation - Count segments with ≥10% slower adjustment 3. Binary search converges when ~50% of segments hit threshold

Interpretation: "Target this time or slower → most segments require PROTECT effort"

Natural Time

The middle reference point - predicted finish time at natural pacing (no deviation).

Including Checkpoint Time

All thresholds include total checkpoint time to represent total race time:

threshold_total = threshold_moving + (num_checkpoints × avg_cp_time)

This ensures thresholds match how users think about total race time (including stops).

Practical Examples

Example 1: Aggressive Target (PUSH Zone)

Athlete Profile: - Natural finish: 20:00:00 - Fitness: Recreational - Climbing: Moderate

Target: 18:00:00 (2 hours faster)

Result: - ΔT = +2:00:00 (need to go faster) - Most segments labeled PUSH (especially flats and easy terrain) - Limited capacity: recreational fitness caps deviation at ~25% (5 hours) - Target is achievable but requires sustained above-threshold effort

Example 2: Conservative Target (PROTECT Zone)

Athlete Profile: - Natural finish: 20:00:00 - Fitness: Trained - Climbing: Strong

Target: 22:30:00 (2.5 hours slower)

Result: - ΔT = -2:30:00 (need to go slower) - Most segments labeled PROTECT - Athlete must actively hold back, especially on climbs where they're naturally strong - Good strategy for ultra-distance energy management

Example 3: Optimal Target (STEADY Zone)

Athlete Profile: - Natural finish: 20:00:00

Target: 19:45:00 to 20:15:00

Result: - ΔT ≈ 0 (within ±15 minutes) - Most/all segments labeled STEADY - Athlete runs at natural ability without significant deviation - Most sustainable and lowest-risk pacing strategy

Constraints and Limitations

Segment-Level Constraints

Each segment has terrain-specific bounds on adjustment:

Steep climbs: Wider range for strong climbers, narrow for conservative
Descents: Hard caps even for skilled athletes (safety/risk limits)
Flat terrain: Medium range, less ability-dependent

Global Constraints

Fitness budget: Total deviation capped by fitness level
Fatigue cost: Late-race adjustments are more expensive
Capacity limits: Can't exceed physiological boundaries

When Targets Are Unachievable

If target requires more deviation than fitness budget allows:

required_deviation > (natural_time × fitness_budget)

The system caps the deviation and warns the user. The calculated plan will get as close as possible but won't fully achieve the target.

UI Indicators

The elevation profile chart displays effort zones: - 🔴 Red segments: PUSH effort required - 🟢 Green segments: STEADY effort (natural pace) - 🔵 Blue segments: PROTECT effort required

Thresholds are shown in the target time input:

Thresholds: Push <18:30:00 | Natural: 20:00:00 | Protect >21:30:00

Comparison with Pace-Based Mode

Aspect	Pace-Based Mode	Target Time Mode
Input	Flat pace (min/km)	Total finish time
Output	Predicted finish time	Required pace strategy
Model	Forward (ability → time)	Inverse (time → effort)
Effort	Implicit	Explicit (labeled)
Optimization	None	Cost-weighted allocation
Use Case	"What can I do?"	"What must I do?"

Best Practices

1. Start with Natural Time

Calculate with your actual abilities first
See what your natural finish time would be
Use this as a reality check for targets

2. Respect Thresholds

Between thresholds: Safest, most sustainable pacing
At PUSH threshold: Requires good fitness and pacing discipline
At PROTECT threshold: Good for ultra-distance or learning races

3. Consider Your Experience

First-time distance: Target PROTECT zone (conservative)
Experienced: Target between STEADY and PUSH threshold
Peak performance: Target PUSH zone (requires perfect execution)

4. Account for Checkpoint Time

Don't forget to include realistic aid station time
More checkpoints = more total time added
Thresholds automatically include this

5. Trust the Labels

PUSH: Expect to feel challenged, monitor for overexertion
STEADY: Should feel sustainable and controlled
PROTECT: Should feel easy, resist urge to go faster

Technical Notes

Optimization Algorithm

The effort allocator uses a greedy cost-weighted distribution rather than true mathematical optimization. This provides: - Fast computation (no iterative solving) - Intuitive results (prioritizes easy terrain) - Respect for hard constraints (physiological limits)

Assumptions

Athlete maintains target pacing strategy throughout race
Conditions match those modeled (weather, terrain, etc.)
Nutrition and hydration are adequate (no bonking)
No mechanical issues or unplanned stops

Limitations

Cannot account for unknown race day conditions
Assumes rational pacing (no emotion-driven surges)
Simplified fatigue model (actual fatigue is complex)
Does not model non-physiological slowdowns (navigation, gear, etc.)

Version History

v1.6.0-target-time-mode (Feb 2, 2026): Initial release
- Target time input mode
- Effort level calculation (PUSH/STEADY/PROTECT)
- Threshold calculation using binary search
- Ability-aware cost weighting
- Checkpoint time integration